The former prime minister said he was not being disloyal, but that it is simply not credible to pretend that his party's position is anything other than "serious".
He warned that even removing Jeremy Corbyn as leader would not solve Labour's problems as the party is "fundamentally" in "the wrong political position".
Mr Corbyn has been criticised in some pro-EU quarters for ordering his MPs to back the triggering of Article 50 to begin Brexit, but has insisted the will of the people in the referendum vote must be respected.
Opinion polls have shown Labour trailing the Tories by up to 18 or 19 points in recent weeks, following the party's humiliating by-election defeat to Theresa May's party in the previously safe seat of Copeland.
In an interview with the Guardian, Mr Blair said: "Labour has got to build out from the Remain vote and reach out to those that are persuadable in the Leave camp.
"It would be a fundamental strategic error to end up trying to go to the Leave camp, and then trying to build out across the other way.
"Then you will end up not persuading the Leave people, and alienating the Remain people.
"At various points over the past 20 to 30 years sometimes it has seemed disloyal to talk about the Labour Party being in bad shape but when it is in the situation it is today - seven years into a Tory government and losing safe Labour seats to the Conservatives - if you want your analysis of politics to retain any credibility, you have got to say the position is serious."
He added: "The position is retrievable, but only if we change. This is not about the personality of the leader.
"In my view, we are in fundamentally the wrong political position. If you stick to that position, even if you change the leader, you will not have a different result."
Mr Blair also said the Prime Minister's pursuit of a so-called "hard Brexit" undoubtedly constituted the "material change" to trigger a second Scottish independence referendum set out in the SNP's 2016 manifesto.
"If Britain stays in Europe you can carry on being Scottish, British and European, but if Britain leaves Europe you can be two of those things, but not all three," he said.
"That is a material change."
Mr Blair went on: "The arguments for the union are very strong, but be in no doubt, I give this very strong warning, there are elements of the Conservative Party and elements of the rightwing media that are perfectly happy with the break-up of the UK."
Mr Blair spoke as he launched the not-for-profit Tony Blair Institute for Global Change, in which he has invested £10 million, with an essay pushing back at the rise in populism and calling for a a renewal of the centre ground in politics.